Question: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 - 11x}{x - 4} = \dfrac{x - 32}{x - 4}$
Answer: Multiply both sides by $x - 4$ $ \dfrac{x^2 - 11x}{x - 4} (x - 4) = \dfrac{x - 32}{x - 4} (x - 4)$ $ x^2 - 11x = x - 32$ Subtract $x - 32$ from both sides: $ x^2 - 11x - (x - 32) = x - 32 - (x - 32)$ $ x^2 - 11x - x + 32 = 0$ $ x^2 - 12x + 32 = 0$ Factor the expression: $ (x - 8)(x - 4) = 0$ Therefore $x = 8$ or $x = 4$ However, the original expression is undefined when $x = 4$. Therefore, the only solution is $x = 8$.